»Write down the equation of an ellipse, that goes through and whose circumscribed* rectangle's area is minimized.«

*http://www.shrani.si/f/3e/vc/1Wz3BdGp/ellipse.gif

(Pretending not knowing that "rectangle" is in fact square.)

Set-up:

Ellipse through : , rectangle's area:

Now, what to differentiate? From the first equation I've also got .